A method for pose calibration of components in a fringe reflection measurement system

Abstract

The present application relates to a kind of pose calibration method of system, to solve the problems of high cost, step cumbersome and large amount of calculation existing in existing calibration method, and provide a kind of pose calibration method of each component in stripe reflection measurement system.The present application includes the following steps:1) prepare laser tracker, camera, display, checkerboard target plate, mirror to be measured, profile frame, optical platform, laser target ball and L-shaped tooling;2) install laser tracker to preset position and adjust, install camera and display, install checkerboard target plate and mirror to be measured to the preset position on optical platform, place laser target ball and L-shaped tooling in the preset position of checkerboard target plate;3) establish world coordinate system, camera coordinate system, display coordinate system, mirror surface coordinate system and checkerboard coordinate system;4) calculate the coordinate transformation matrix of other coordinate systems relative to world coordinate system, to obtain the pose relationship of each component in stripe reflection measurement system.

Description

Technical Field

[0001] This invention relates to a system pose calibration method, specifically to a pose calibration method for each component in a fringe reflectance measurement system. Background Technology

[0002] Optical aspherical or freeform surfaces simplify the structure of optical systems and improve image quality. With the continuous development of space optics and astronomical optics, the demand for larger aperture and higher precision mirrors in related fields is constantly increasing. As a core component of modern reflective optical systems, the size and surface precision of large-aperture mirrors directly affect the system's resolving power. Furthermore, the fabrication of large-aperture mirrors requires the use of high-precision processing equipment and testing methods.

[0003] Currently, the fringe reflection method plays a crucial role in the inspection process of large-aperture mirrors, especially in the transition from grinding to polishing, namely the fine grinding stage in the later stage of grinding and the rough polishing stage in the early stage of polishing. During this period, the local surface shape error of large-aperture mirrors typically exceeds 10 μm. Conventional profilometers and interferometry are insufficient for efficiently and accurately inspecting mirrors in this transitional stage. The fringe reflection method, with its sub-micron level accuracy, non-contact measurement method, highly efficient inspection process, and large dynamic range, can accurately measure mirrors during the grinding transition.

[0004] A laser tracker is a device used to track targets, using a laser beam to measure the position and motion of the target object. Its working principle involves emitting a narrow, stable laser beam and then using a photodetector to receive the light signal reflected back from the target object. When the laser beam strikes the target object, a portion of the beam is reflected back and received by the receiver. The receiver converts the received light signal into an electrical signal and sends it to a signal processing unit for analysis. By analyzing the received light signal, the signal processing unit can determine the position and motion information of the target object. Specifically, by utilizing the wavelength and optical path difference principle of the laser, the distance between the target object and the laser tracker can be calculated.

[0005] Based on the working principle of fringe reflectance measurement systems, the reconstruction of the three-dimensional shape of an object's surface relies on the phase information of corresponding points on the camera and display. By precisely calibrating the relationship between phase information and geometric position, researchers can obtain high-precision measurement results. Accurate phase information is crucial to the final measurement results because even small deviations in relative information can significantly affect the results. Therefore, sub-micron or even nanometer-level geometric position calibration is essential in fringe reflectance systems. This accurate calibration ensures the reliability of the final measurement results and allows fringe reflectance measurement technology to perform optimally in various application fields.

[0006] Furthermore, Chinese invention patent CN107883870A discloses a global calibration method based on a binocular vision system and a laser tracker measurement system. Specifically, it involves: first, fabricating a rigid 3D target with circular markers for the binocular vision system on surface A and a laser tracker measurement target sphere on surface B; then, establishing the coordinate systems of surface A and surface B of the 3D target; calculating the transformation relationship between the coordinate system of surface A of the 3D target and the coordinate system of the left camera of the binocular vision system, and the transformation relationship between the coordinate system of surface B of the 3D target and the world coordinate system of the laser tracker; based on the transformation relationships calculated in the previous step, calculating the transformation relationship between the coordinate systems of surface A and surface B; and finally, calculating the transformation relationship between the coordinate system of the left camera of the global calibration binocular vision system and the world coordinate system of the laser tracker. However, this invention patent has the following shortcomings:

[0007] 1) The three-dimensional target in this invention has a complex structure, which is difficult to manufacture and requires special customization; in addition, five holes are opened on the A side of the three-dimensional target, five holes are opened on the B side, and five laser tracker target balls are fixed on the B side, which is costly.

[0008] 2) During calibration, the 3D target needs to be moved multiple times. A coordinate transformation matrix is ​​calculated for each movement position. Each movement is equivalent to the hole on surface A moving five times and the laser tracker target ball on surface B moving five times. The process is tedious.

[0009] 3) The circular hole on the A side of the 3D target will become an ellipse after being photographed by the camera. Extracting the center of the circle requires an additional algorithm, and multiple movements will result in a large amount of computation. Summary of the Invention

[0010] The purpose of this invention is to solve the problems of high cost, cumbersome steps and large amount of calculation in existing calibration methods, and to provide a method for calibrating the pose of each component in a stripe reflection measurement system.

[0011] To achieve the above objectives, the technical solution provided by this invention is:

[0012] A method for calibrating the pose of each component in a fringe reflectance measurement system, characterized by the following steps:

[0013] Step 1: Prepare the laser tracker, camera, monitor, profile frame, and optical platform; prepare the mirror to be tested; prepare the following calibration components: checkerboard target plate, L-shaped fixture, and laser target ball compatible with the laser tracker;

[0014] Step 2: Install the laser tracker to the preset position and adjust it to the ready state; install the camera and monitor to the preset position on the profile frame, and install the mirror to be tested to the preset position on the optical platform; install the checkerboard target plate to the preset position on the optical platform, and then install the L-shaped fixture and laser target ball to the preset position on the checkerboard target plate to form a stripe reflection measurement system;

[0015] Step 3: Select any point on the optical platform and establish the world coordinate system O. W -X W Y W Z W Based on the camera's physical position and optical axis direction, establish the camera coordinate system O. C -X C Y C Z C Using a laser tracker and a laser target sphere, a plane of the display screen and a plane of the mirror under test are fitted, respectively. A normal vector and an origin are determined for the plane of the mirror under test and the plane of the display screen, respectively. A display coordinate system O is then established based on the normal vector and the origin. L -X L Y L Z L and mirror coordinate system O M -X M Y M Z M Take at least three top-view photographs of the checkerboard target board using a camera, and establish a checkerboard coordinate system O. Q -X Q Y Q Z Q ;

[0016] Step 4: Using the display coordinate system O L -X L Y L Z L Using the origin and three coordinate axes as references, calculate the display coordinate system O. L -X L Y L Z L Relative to world coordinate system O W -X W Y W Z W The rotation matrix R1 and translation vector T1 are used to obtain the display coordinate system O. L -X L Y L Z L With world coordinate system O W -X W Y W Z WThe coordinate mapping relationship between them;

[0017] Step 5: Select one of the upper or lower surfaces of the mirror under test. Use a laser tracker with a laser target sphere to obtain the coordinates of at least three different points on this surface, and calculate the plane equation of this surface. Then, based on the plane equation, the coordinates of at least three points on the surface of the mirror under test, and the world coordinate system O... W -X W Y W Z W and mirror coordinate system O M -X M Y M Z M Calculate the mirror coordinate system O M -X M Y M Z M Relative to world coordinate system O W -X W Y W Z W The rotation matrix R2 and translation vector T2 are used to obtain the mirror coordinate system O. M -X M Y M Z M With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them;

[0018] Step 6: Using at least three photos taken by the camera in Step 3, calculate the checkerboard coordinate system O. Q -X Q Y Q Z Q Relative to camera coordinate system O C -X C Y C Z C The rotation matrix R3 and translation vector T3 are used to obtain the chessboard coordinate system O. Q -X Q Y Q Z Q With camera coordinate system O C -X C Y C Z C The coordinate mapping relationship between them;

[0019] Step 7: Using the photos taken by the camera in Step 3, obtain the coordinates of the contact point between the laser target ball and the checkerboard target plate, and calculate the checkerboard coordinate system O. Q -X Q Y Q Z Qwith respect to the world coordinate system O W -X W Y W Z W , the rotation matrix R4 and translation vector T4 are obtained, so as to obtain the checkerboard coordinate system O Q -X Q Y Q Z Q and the world coordinate system O W -X W Y W Z W the coordinate mapping relationship therebetween;

[0020] Step 8: using the two sets of rotation matrices and translation vectors obtained in step 6 and step 7, calculate the camera coordinate system O C -X C Y C Z C with respect to the world coordinate system O W -X W Y W Z W , the rotation matrix R5 and translation vector T5 are obtained, so as to obtain the camera coordinate system O C -X C Y C Z C and the world coordinate system O W -X W Y W Z W the coordinate mapping relationship therebetween, and complete the pose calibration of the fringe reflection measurement system.

[0021] Further, in step 2, the step of "installing the laser tracker at a preset position and adjusting the laser tracker to a ready state" specifically comprises: mounting the laser tracker on a laser tracker support and connecting the laser tracker to a computer, then adjusting the laser tracker in horizontal and vertical directions according to the angular deviations in horizontal and vertical directions displayed on the laser tracker console of the laser tracker until the offsets in both horizontal and vertical directions are less than or equal to 3°, then preheating the laser tracker by using software matched with the laser tracker in the computer, so as to enable the laser tracker to enter the ready state.

[0022] Further, in step 2, the step of "mounting the camera and the display at preset positions on a profile frame, and mounting the mirror to be measured at a preset position on an optical platform" specifically comprises:

[0023] 1) fixing the mirror to be measured on the optical platform and limiting the position of the mirror by using a square limiting member to prevent the mirror to be measured from moving;

[0024] 2) Fix the monitor to one end of the profile frame and adjust its height and angle to the ready position. Then fix the camera to the other end of the profile frame and adjust its height and angle to the ready position.

[0025] Furthermore, in step 2, “installing the L-shaped fixture and the laser target ball to the preset position on the checkerboard target plate” specifically means: fixing the L-shaped fixture at a measurement corner point of the checkerboard target plate, and fixing the laser target ball on the checkerboard target plate and contacting the two right-angled sides of the L-shaped fixture.

[0026] Furthermore, in step 3, the world coordinate system O W -X W Y W Z W Display coordinate system O L -X L Y L Z L Mirror coordinate system O M -X M Y M Z M chessboard coordinate system O Q -X Q Y Q Z Q and camera coordinate system O C -X C Y C Z C All are three-dimensional rectangular coordinate systems, with the world coordinate system O. W -X W Y W Z W The x and y axes lie in the plane containing the upper surface of the optical platform, and the z axis is perpendicular to the upper surface of the optical platform; the display coordinate system O L -X L Y L Z L The origin is the center point of the monitor screen, and the monitor coordinate system O L -X L Y L Z L The z-axis is perpendicular to the screen and points outwards; the x and y axes are in any direction within the plane of the screen; mirror coordinate system O M -X M Y M Z M The origin is the geometric center of the mirror to be tested, and the directions of its x, y, and z axes are perpendicular to the world coordinate system O. W -X W Y W Z W The x, y, and z axes are in the same direction; the checkerboard coordinate system O Q -XQ Y Q Z Q The origin is one corner endpoint of the checkerboard target board; the camera coordinate system O C -X C Y C Z C The origin is the optical center of the camera, where the camera coordinate system O C -X C Y C Z C The z-axis direction is parallel to the optical axis direction of the camera.

[0027] Furthermore, in step 4, a four-dimensional column vector C is defined. WorldCoordinate World coordinate system O W -X W Y W Z W The coordinates of any point P in the vector, and the four-dimensional column vector C. MonitorCoordinate C MirrorCoordinate C CheckerCoordinate C CameraCoordinate The display coordinate system O is represented sequentially. L -X L Y L Z L Mirror coordinate system O M -X M Y M Z M chessboard coordinate system O Q -X Q Y Q Z Q and camera coordinate system O C -X C Y C Z C If the coordinates of the point corresponding to point P are given, then C WorldCoordinate With C MonitorCoordinate The coordinate mapping relationship between them is as follows:

[0028]

[0029] In step 5, C WorldCoordinate With C MirrorCoordinate The coordinate mapping relationship between them is as follows:

[0030]

[0031] In step 6, C CameraCoordinate With C CheckerCoordinate The coordinate mapping relationship between them is as follows:

[0032]

[0033] In step 7, C WorldCoordinate With C CheckerCoordinate The coordinate mapping relationship between them is as follows:

[0034]

[0035] In step 8, C WorldCoordinate With C CameraCoordinate The coordinate mapping relationship between them is as follows:

[0036]

[0037] Where C WorldCoordinate =(x W ,y W ,z W ,1) T ;

[0038] C MonitorCoordinate =(x L ,y L ,z L ,1) T ;

[0039] C MirrorCoordinate =(x M ,y M ,z M ,1) T ;

[0040] C CheckerCoordinate =(x Q ,y Q ,z Q ,1) T ;

[0041] C CameraCoordinate =(x C ,y C ,z C ,1) T ;

[0042] R1, R2, R3, R4 and R5 are all rotation matrices, and all are third-order square matrices;

[0043] T1, T2, T3, T4, and T5 are all translation vectors, and are all three-dimensional column vectors;

[0044] All are block matrices of the same type and coordinate transformation matrices, i = 1, 2, 3, 4, 5.

[0045] Furthermore, the T1 = (x t1 ,y t1 ,z t1 ) T T2 = (x t2,y t2 ,z t2 ) T T3 = (x t3 ,y t3 ,z t3 ) T T4 = (x t4 ,y t4 ,z t4 ) T T5 = (x t5 ,y t5 ,z t5 ) T x ti y ti z ti The values ​​are the x, y, and z directions of the new coordinate system relative to the old coordinate system, respectively, i = 1, 2, 3, 4, 5.

[0046] Furthermore, the R i =R x (θ i )R y (φ i )R z (ψ i );

[0047] in

[0048]

[0049]

[0050] θ i Let φ be the x-axis rotation angle of the new coordinate system relative to the old coordinate system. i Let ψ be the y-axis rotation angle of the new coordinate system relative to the old coordinate system. i R is the rotation angle of the new coordinate system relative to the old coordinate system along the z-axis. x (θ i R is the rotation matrix in the x-direction of the new coordinate system relative to the old coordinate system. y (φ i R is the rotation matrix in the y-direction of the new coordinate system relative to the old coordinate system. z (ψ i ) is the rotation matrix in the z-direction of the new coordinate system relative to the old coordinate system, i = 1, 2, 3, 4, 5.

[0051] Furthermore, in step 3, the display coordinate system O is established. L -X L Y L Z L The specific steps are as follows:

[0052] 1) Divide the monitor screen into four equal parts in both the horizontal and vertical directions using six grid lines, with each grid line being 1 pixel wide;

[0053] 2) Using a laser tracker, a laser target sphere, and a computer, the plane containing the nine intersection points of the six grid lines is fitted, and the center point of the screen and the normal vector of the plane are determined;

[0054] 3) Use the center point of the screen as the monitor coordinate system O L -X L Y L Z L The origin of the plane is used as the normal vector of the display coordinate system O. L -X L Y L Z L Then, arbitrarily select the x and y axes to establish the display coordinate system O. L -X L Y L Z L .

[0055] Furthermore, the display is an LCD display with a screen resolution of 1280×800, the camera is a CCD camera; the size of the checkerboard target plate is 15mm×15mm, and the diameter of the laser target ball is 0.5 inches.

[0056] Compared with the prior art, the beneficial effects of the present invention are:

[0057] 1. The pose calibration method of each component in the fringe reflectance measurement system provided by the present invention adopts a calibration method that combines a laser tracker, a checkerboard target plate and a calibration component set on the checkerboard target plate, and achieves high-precision submicron level calibration results. It can complete accurate measurement and solve the problem of solving the coordinate transformation matrix between each component in the fringe reflectance measurement system without designing complex marker targets.

[0058] 2. The pose calibration method for each component in the fringe reflection measurement system provided by this invention uses a simple device, which reduces the calibration cost and improves the calibration accuracy. This calibration method has a wide range of applications and can be applied to various fields that require high-precision measurement, such as engineering measurement, robot navigation, virtual reality and other fields.

[0059] 3. The pose calibration method for each component in the stripe reflection measurement system provided by the present invention has the advantages of simple operation and low computational load. Attached Figure Description

[0060] Figure 1This is a schematic diagram showing the positional relationship between the laser tracker, camera, display, test mirror, and checkerboard target plate in the pose calibration method of the components in the fringe reflection measurement system of the present invention.

[0061] Figure 2 This is a schematic diagram of the structure of the laser tracker, laser tracker support, and laser tracker control console in the pose calibration method of each component in the fringe reflection measurement system of the present invention;

[0062] Figure 3 This is a schematic diagram of the structure of the mirror under test, the square limiting component, and the optical platform in the pose calibration method of each component in the fringe reflection measurement system of the present invention;

[0063] Figure 4 This is a schematic diagram of the structure of the checkerboard target plate, L-shaped tooling, and laser target ball in the pose calibration method of each component in the stripe reflection measurement system of the present invention.

[0064] Figures 1-4 Explanation of reference numerals in the attached figures:

[0065] 11-Laser tracker; 12-Laser tracker bracket; 13-Laser tracker control console; 2-Camera; 3-Display; 4-Checkerboard target plate; 401-L-shaped fixture; 402-Laser target ball; 5-Mirror to be tested; 501-Square limiting component; 6-Optical platform. Detailed Implementation

[0066] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0067] A method for calibrating the pose of components in a fringe reflectance measurement system, using a device position relationship diagram and schematic diagram (see attached). Figures 1-4 The fringe reflectance measurement system includes an optical platform 6, a laser tracker 11, a camera 2, and a display 3, as well as a laser tracker bracket 12 and a profile frame. The laser tracker 11 is mounted on the laser tracker bracket 12, and a laser tracker control console 13 is provided on the laser tracker 11. The camera 2 and the display 3 are respectively mounted at both ends of the profile frame. The mirror under test 5 is set on the optical platform 6.

[0068] This invention primarily calibrates the poses of the laser tracker 11, camera 2, and display 3 in the stripe reflection measurement system, as well as the pose of the mirror 5 under test. Specifically, a calibration component mounted on the optical platform 6 is used in conjunction with the laser tracker 11 and camera 2 for calibration. The calibration component includes a checkerboard target plate 4 mounted on the optical platform 6 and a laser target ball 402 mounted on the checkerboard target plate 4.

[0069] The pose calibration method of the present invention includes the following steps:

[0070] Step 1: Prepare a laser tracker 11, a camera 2, a display 3, a profile frame and an optical platform 6; prepare a mirror 5 to be measured; prepare the following calibration components: a checkerboard target plate 4, an L-shaped tooling 401 and a laser target ball 402 matching the laser tracker 11; wherein the display 3 is an LCD display with a screen resolution of 1280×800, the camera is a CCD camera with a resolution of 1920×1200, a lens focal length of 50mm, and the size of the checkerboard target plate 4 is 15mm×15mm;

[0071] Step 2: Mount the laser tracker 11 on a laser tracker support 12 and connect it to a computer, then adjust the laser tracker in horizontal and vertical directions according to the angular deviations in horizontal and vertical directions displayed on the laser tracker console of the laser tracker until the offsets in both horizontal and vertical directions are less than or equal to 3°, then preheat the laser tracker 11 using software matching it in the computer to make it enter a ready state. Fix the display 3 at one end of the profile frame and adjust its height and angle to the ready state, then fix the camera 2 at the other end of the profile frame and adjust its height and angle to the ready state, fix the mirror 5 to be measured on the optical platform and limit it with a square limiting member 501 to prevent the movement of the mirror 5 to be measured, mount the checkerboard target plate 4 at a preset position on the optical platform, fix the L-shaped tooling 401 at a measuring corner point of the checkerboard target plate 4, and fix the laser target ball 402 on the checkerboard target plate 4 and make it contact with two right-angled sides of the L-shaped tooling 401. All the above components form a fringe reflection measurement system;

[0072] Step 3: Select any point on the optical platform 6 and establish a world coordinate system O W -X W Y W Z W ; establish a camera coordinate system O according to the body position and optical axis direction of the camera 2 C -X C Y C Z C ; use the laser tracker 11 in cooperation with the laser target ball 402 to respectively fit the screen of the display 3 and a plane of the mirror 5 to be measured, and respectively determine a normal vector and an origin of the plane where the mirror 5 to be measured and the screen of the display 3 are located, and establish a display coordinate system O based on the normal vector and the origin L -X L Y L Z L and a mirror surface coordinate system O M -X M Y M Z M ; use the camera 2 to take fifteen top-view full pictures of the checkerboard target plate 4, and establish a checkerboard coordinate system OQ -X Q Y Q Z Q ;

[0073] World coordinate system O W -X W Y W Z W Display coordinate system O L -X L Y L Z L Mirror coordinate system O M -X M Y M Z M chessboard coordinate system O Q -X Q Y Q Z Q and camera coordinate system O C -X C Y C Z C All are three-dimensional rectangular coordinate systems, with the world coordinate system O. W -X W Y W Z W The x and y axes lie in the plane containing the upper surface of the optical platform 6, and the z axis is perpendicular to the upper surface of the optical platform 6; the display coordinate system O L -X L Y L Z L The origin is the center point of the screen of monitor 3, and the monitor coordinate system O L -X L Y L Z L The z-axis is perpendicular to the screen and points outwards; the x and y axes are in any direction within the plane of the screen; mirror coordinate system O M -X M Y M Z M The origin is the geometric center of the mirror 5 to be tested, and the directions of its x, y, and z axes are perpendicular to the world coordinate system O. W -X W Y W Z W The x, y, and z axes are in the same direction; the checkerboard coordinate system O Q -X Q Y Q Z Q The origin is one corner endpoint of the checkerboard target board 4; the camera coordinate system O C -X C Y C Z CThe origin is the optical center of camera 2, where the camera coordinate system O C -X C Y C Z C The z-axis direction is parallel to the optical axis direction of camera 2.

[0074] Step 4: Using the display coordinate system O L -X L Y L Z L Using the origin and three coordinate axes as references, calculate the display coordinate system O. L -X L Y L Z L Relative to world coordinate system O W -X W Y W Z W The rotation matrix R1 and translation vector T1 are used to obtain the display coordinate system O. L -X L Y L Z L With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them;

[0075] Establish display coordinate system O L -X L Y L Z L The specific steps are as follows:

[0076] 1) Divide the screen of display 3 into four equal parts in both the horizontal and vertical directions using six grid lines, with each grid line having a width of 1 pixel;

[0077] 2) Using the laser tracker 11, the laser target sphere 402, and the computer, the plane containing the nine intersection points of the six grid lines is fitted, and the center point of the screen and the normal vector of the plane are determined;

[0078] 3) Use the center point of the screen as the monitor coordinate system O L -X L Y L Z L The origin of the plane is used as the normal vector of the display coordinate system O. L -X L Y L Z L Then, arbitrarily select the x and y axes to establish the display coordinate system O. L -X L Y L ZL ;

[0079] Step 5: Select the upper surface of the mirror 5 to be tested, and use the laser tracker 11 in conjunction with the laser target sphere 402 to obtain the coordinates of three different points on the plane, and calculate the plane equation of the surface; then, based on the plane equation, the coordinates of the three points on the plane, and the world coordinate system O... W -X W Y W Z W and mirror coordinate system O M -X M Y M Z M Calculate the mirror coordinate system O M -X M Y M Z M Relative to world coordinate system O W -X W Y W Z W The rotation matrix R2 and translation vector T2 are used to obtain the mirror coordinate system O. M -X M Y M Z M With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them;

[0080] Step 6: Using the fifteen photos taken by camera 2 in step 3, calculate the checkerboard coordinate system O using MATLAB. Q -X Q Y Q Z Q Relative to world coordinate system O W -X W Y W Z W The rotation matrix R3 and translation vector T3 are used to obtain the chessboard coordinate system O. Q -X Q Y Q Z Q With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them;

[0081] Step 7: Using the first of the fifteen photos taken by camera 2 in step 3, obtain the coordinates of the contact point between the laser target ball 402 and the checkerboard target plate 4, and calculate the checkerboard coordinate system O. Q -X Q Y QZ Q Relative to camera coordinate system O C -X C Y C Z C The rotation matrix R4 and translation vector T4 are used to obtain the chessboard coordinate system O. Q -X Q Y Q Z Q With camera coordinate system O C -X C Y C Z C The coordinate mapping relationship between them;

[0082] Step 8: Using the two sets of rotation matrices and translation vectors obtained in Steps 6 and 7, calculate the camera coordinate system O. C -X C Y C Z C Relative to world coordinate system O W -X W Y W Z W The rotation matrix R5 and translation vector T5 are used to obtain the camera coordinate system O. C -X C Y C Z C With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them is used to complete the pose calibration of the fringe reflection measurement system.

[0083] In the calibration method of this invention, the display 3 world coordinate system O W -X W Y W Z W Position calibration can be achieved using a 0.5-inch laser target ball 402, when the display coordinate system O L -X L Y L Z L Then, the display coordinate system O can be obtained. L -X L Y L Z L Relative to world coordinate system O W -X W Y W Z W coordinate mapping relationship

[0084]

[0085] Since the optical plane of the mirror under test is not strictly parallel to the optical platform, calibration of the mirror surface is necessary. Calibration measurements were performed using a laser tracker 11 and its matching 0.5-inch laser target sphere 402. Based on the measured three-dimensional spatial coordinates of the points in the world coordinate system, the plane equation of the optical plane of the mirror under test relative to the world coordinate system was obtained using the least squares method fitted in MATLAB.

[0086] z=-0.0057374x+0.015397y+9.7539

[0087] Then the mirror coordinate system O can be calculated. M -X M Y M Z M Relative to world coordinate system O W -X W Y W Z W coordinate mapping relationship

[0088]

[0089] The coordinate system O of the chessboard grid needs to be calculated next. Q -X Q Y Q Z Q and camera coordinate system O C -X C Y C Z C Relative to world coordinate system O W -X W Y W Z W The coordinate mapping relationship, due to the camera coordinate system O C -X C Y C Z C The origin is located at the optical center of camera 2, which cannot be directly measured. It needs to be calculated using Zhang Zhengyou's calibration method. The reprojection error of this method is less than or equal to 0.04 pixels. The specific steps are as follows:

[0090] 1) Fix the checkerboard target plate 4 on the optical platform, and use the laser tracker 11 to measure the coordinates of several preset corner points on the checkerboard target plate 4 in the world coordinate system O. W -X W Y W Z W The coordinates below;

[0091] 2) Measurements are performed using a 0.5-inch laser target ball 402 in conjunction with the laser tracker 11. The actual measurement point is the contact point between the laser target ball 402 and the checkerboard target plate 4, not the coordinates of a specific corner of the actual checkerboard target plate 4. The L-shaped fixture 401 is clamped at a measurement corner of the checkerboard. The precise coordinates of the checkerboard measurement corner point are obtained by adding or subtracting the radius of the 0.5-inch target ball from the measured world coordinates. The world coordinates of the contact point of the laser target ball 402 and the checkerboard corner point are shown in Tables 1 and 2. The checkerboard world coordinates for number 1 are in the checkerboard coordinate system O. Q -X Q Y Q Z Q The coordinates of the origin are shown in Table 1. The results will vary depending on the different scenarios, devices, and placement methods.

[0092] Table 1 World Coordinates of Contact Points of Laser Target Ball

[0093]

[0094] Table 2 corresponds to the chessboard world coordinates table in Table 1.

[0095]

[0096] 3) After measuring the corner points of the checkerboard at this location, use camera 2 to take pictures of the checkerboard at this location. At least three pictures need to be taken. To ensure measurement accuracy, this embodiment takes fifteen pictures of the checkerboard at different locations. Import the obtained checkerboard pictures into MATLAB for camera calibration to obtain the intrinsic parameter matrix N of camera 2.

[0097] Where f is the focal length of camera 2, dx and dy are the pixel size of the camera, and generally dx = dy. f / dx and f / dy represent the equivalent focal length of camera 2 in the x and y directions, respectively, and u0 and v0 represent the horizontal and vertical coordinates of the camera principal point, respectively.

[0098] 4) Export the rotation matrix and translation vector of the chessboard at this location using MATLAB to obtain the chessboard coordinate system O. Q -X Q Y Q Z Q Relative to camera coordinate system O C -X C Y C Z C The rotation matrix R3 and translation vector T3 are obtained. Here, the CameraCalibrator toolbox in MATLAB is used for processing, and the final result is...

[0099]

[0100] 5) Using the measured coordinates of position 1, the rotation matrix R4 and translation vector T4 of the checkerboard coordinate system relative to the world coordinate system can be obtained.

[0101]

[0102] Combining formulas [1][2][3][4], we can obtain...

[0103]

[0104] In equations [1][2][3][4][5], C WorldCoordinate C MonitorCoordinate C MirrorCoordinate C CheckerCoordinate C CameraCoordinate All are four-dimensional column vectors, and satisfy the following conditions:

[0105] C WorldCoordinate =(x W ,y W ,z W ,1) T ;

[0106] C MonitorCoordinate =(x L ,y L ,z L ,1) T ;

[0107] C MirrorCoordinate =(x M ,y M ,z M ,1) T ;

[0108] C CheckerCoordinate =(x Q ,y Q ,z Q ,1) T ;

[0109] C CameraCoordinate =(x C ,y C ,z C ,1) T ;

[0110] The first three elements of each column vector represent the three-dimensional coordinates of the corresponding point, and the fourth element is always 1. This is to ensure the homogeneity of the entire formula.

[0111] R1, R2, R3, R4 and R5 are all rotation matrices, and all are third-order square matrices;

[0112] T1, T2, T3, T4, and T5 are all translation vectors, and are all three-dimensional column vectors;

[0113] All are block matrices of the same type and coordinate transformation matrices, i = 1, 2, 3, 4, 5.

[0114] T1=(x t1 ,y t1 ,z t1 ) T T2 = (x t2 ,y t2 ,z t2 ) T T3 = (x t3 ,y t3 ,z t3 ) T T4 = (x t4 ,y t4 ,z t4 ) T T5 = (x t5 ,y t5 ,z t5 ) T x ti y ti z ti The values ​​are the x, y, and z directions of the new coordinate system relative to the old coordinate system, i = 1, 2, 3, 4, 5.

[0115] R i =R x (θ i )R y (φ i )R z (ψ i );

[0116] in

[0117]

[0118]

[0119] θ i Let φ be the x-axis rotation angle of the new coordinate system relative to the old coordinate system. i Let ψ be the y-axis rotation angle of the new coordinate system relative to the old coordinate system. i R is the rotation angle of the new coordinate system relative to the old coordinate system along the z-axis. x (θ i R is the rotation matrix in the x-direction of the new coordinate system relative to the old coordinate system. y (φ iR is the rotation matrix in the y-direction of the new coordinate system relative to the old coordinate system. z (ψ i ) is the rotation matrix in the z-direction of the new coordinate system relative to the old coordinate system, i = 1, 2, 3, 4, 5.

[0120] From [1][2][3][4][5], we can know that the world coordinate system O W -X W Y W Z W Display coordinate system O L -X L Y L Z L Mirror coordinate system O M -X M Y M Z M chessboard coordinate system O Q -X Q Y Q Z Q and camera coordinate system O C -X C Y C Z C The mapping relationship between them allows for arbitrary coordinate transformations and also provides accurate geometric position data for subsequent gradient integration and wavefront reconstruction.

[0121] The pose calibration method for each component in the fringe reflectance measurement system provided in this embodiment adopts a calibration method that combines a laser tracker, a checkerboard target plate, and calibration components set on the checkerboard target plate. This achieves high-precision sub-micron level calibration results. It can complete accurate measurements and solve the problem of solving the coordinate transformation matrix between the various components in the fringe reflectance measurement system without designing complex marker targets. At the same time, the device used is simple, reducing calibration costs and improving calibration accuracy. This calibration method has wide application value and can be applied to various fields that require high-precision measurement, such as engineering surveying, robot navigation, and virtual reality.

[0122] It should be noted that the above are only specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for calibrating the pose of each component in a fringe reflectance measurement system, characterized in that, Includes the following steps: Step 1: Prepare the laser tracker (11), camera (2), display (3), profile frame and optical platform (6); prepare the mirror to be tested (5); prepare the following calibration components: checkerboard target plate (4), L-shaped fixture (401) and laser target ball (402) matching the laser tracker (11); Step 2: Install the laser tracker (11) to the preset position and adjust the laser tracker (11) to the ready state; install the camera (2) and the display (3) to the preset position on the profile frame, and install the mirror to be tested (5) to the preset position on the optical platform (6); install the checkerboard target plate (4) to the preset position on the optical platform (6), and then install the L-shaped fixture (401) and the laser target ball (402) to the preset position on the checkerboard target plate (4) to form a stripe reflection measurement system; Step 3: Select any point on the optical platform (6) and establish the world coordinate system O. W -X W Y W Z W Based on the position of the camera (2) and the direction of its optical axis, establish the camera coordinate system O. C -X C Y C Z C Using a laser tracker (11) and a laser target ball (402), a plane of the screen of the display (3) and a plane of the mirror under test (5) are fitted respectively. A normal vector and an origin of the plane of the mirror under test (5) and the plane of the screen of the display (3) are determined respectively. The display coordinate system O is established based on the normal vector and the origin. L -X L Y L Z L and mirror coordinate system O M -X M Y M Z M Use camera (2) to take at least three top-view photos of the checkerboard target board (4) and establish a checkerboard coordinate system O. Q -X Q Y Q Z Q ; Step 4: Using the display coordinate system O L -X L Y L Z L Using the origin and three coordinate axes as references, calculate the display coordinate system O. L -X L Y L Z L Relative to world coordinate system O W -X W Y W Z W The rotation matrix R1 and translation vector T1 are used to obtain the display coordinate system O. L -X L Y L Z L With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them; Step 5: Select one of the upper or lower surfaces of the mirror (5) to be tested, and use a laser tracker (11) in conjunction with a laser target ball (402) to obtain the coordinates of at least three different points on the surface, and calculate the plane equation of the surface; then, based on the plane equation, the coordinates of at least three points on the surface of the mirror (5) to be tested, and the world coordinate system O W -X W Y W Z W and mirror coordinate system O M -X M Y M Z M Calculate the mirror coordinate system O M -X M Y M Z M Relative to world coordinate system O W -X W Y W Z W The rotation matrix R2 and translation vector T2 are used to obtain the mirror coordinate system O. M -X M Y M Z M With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them; Step 6: Using at least three photos taken by camera (2) in step 3, calculate the checkerboard coordinate system O. Q -X Q Y Q Z Q Relative to camera coordinate system O C -X C Y C Z C The rotation matrix R3 and translation vector T3 are used to obtain the chessboard coordinate system O. Q -X Q Y Q Z Q With camera coordinate system O C -X C Y C Z C The coordinate mapping relationship between them; Step 7: Using the photos taken by camera (2) in step 3, obtain the coordinates of the contact point between the laser target ball (402) and the checkerboard target plate (4), and calculate the checkerboard coordinate system O. Q -X Q Y Q Z Q Relative to world coordinate system O W -X W Y W Z W The rotation matrix R4 and translation vector T4 are used to obtain the chessboard coordinate system O. Q -X Q Y Q Z Q With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them; Step 8: Using the two sets of rotation matrices and translation vectors obtained in Steps 6 and 7, calculate the camera coordinate system O. C -X C Y C Z C Relative to world coordinate system O W -X W Y W Z W The rotation matrix R5 and translation vector T5 are used to obtain the camera coordinate system O. C -X C Y C Z C With world coordinate system O W -X W Y W Z W The coordinate mapping relationship between them is used to complete the pose calibration of the fringe reflection measurement system.

2. The pose calibration method for each component in the fringe reflectance measurement system according to claim 1, characterized in that, Step 2, "Install the laser tracker (11) to the preset position and adjust the laser tracker (11) to the ready state," specifically means: Install the laser tracker (11) onto the laser tracker bracket (12), and then adjust the laser tracker (11) in the horizontal and vertical directions according to the angle deviation in the horizontal and vertical directions displayed on the laser tracker control console (13) of the laser tracker (11) until the offset in the horizontal and vertical directions is less than or equal to 3°. Then preheat the laser tracker (11) to make it ready.

3. The pose calibration method for each component in the fringe reflectance measurement system according to claim 1, characterized in that, Step 2, "installing the camera (2) and the display (3) in the preset positions on the profile frame, and installing the mirror to be tested (5) in the preset positions on the optical platform (6)," specifically means: 1) Fix the mirror to be tested (5) on the optical platform (6) and limit it with a square limiting piece (501) to prevent the mirror to be tested (5) from moving; 2) Fix the monitor (3) to one end of the profile frame and adjust its height and angle to the ready state, then fix the camera (2) to the other end of the profile frame and adjust its height and angle to the ready state.

4. The pose calibration method for each component in the fringe reflectance measurement system according to claim 1, characterized in that, In step 2, the L-shaped fixture (401) and the laser target ball (402) are installed at the preset positions on the checkerboard target plate (4) as follows: The L-shaped fixture (401) is fixed at one measuring corner of the checkerboard target plate (4), and the laser target ball (402) is fixed on the checkerboard target plate (4) and contacts the two right-angled sides of the L-shaped fixture (401).

5. The pose calibration method for each component in the fringe reflectance measurement system according to any one of claims 1-4, characterized in that: In step 3, the world coordinate system O W -X W Y W Z W Display coordinate system O L -X L Y L Z L Mirror coordinate system O M -X M Y M Z M chessboard coordinate system O Q -X Q Y Q Z Q and camera coordinate system O C -X C Y C Z C All are three-dimensional rectangular coordinate systems, with the world coordinate system O. W -X W Y W Z W The x and y axes lie in the plane containing the upper surface of the optical platform (6), and the z axis is perpendicular to the upper surface of the optical platform (6); the display coordinate system O L -X L Y L Z L The origin is the center point of the screen of the monitor (3), and the monitor coordinate system O L -X L Y L Z L The z-axis is perpendicular to the screen and points outwards; the x and y axes are in any direction within the plane of the screen; mirror coordinate system O M -X M Y M Z M The origin is the geometric center of the mirror to be tested (5), and the directions of its x, y, and z axes are perpendicular to the world coordinate system O. W -X W Y W Z W The x, y, and z axes are in the same direction; the checkerboard coordinate system O Q -X Q Y Q Z Q The origin is one corner endpoint of the checkerboard target board (4); the camera coordinate system O C -X C Y C Z C The origin is the optical center of camera (2), where the camera coordinate system O C -X C Y C Z C The z-axis direction is parallel to the optical axis direction of the camera (2).

6. The pose calibration method for each component in the fringe reflectance measurement system according to claim 5, characterized in that: In step 4, a four-dimensional column vector C is defined. WorldCoordinate World coordinate system O W -X W Y W Z W The coordinates of any point P in the vector, and the four-dimensional column vector C. MonitorCoordinate C MirrorCoordinate C CheckerCoordinate C CameraCoordinate The display coordinate system O is represented sequentially. L -X L Y L Z L Mirror coordinate system O M -X M Y M Z M chessboard coordinate system O Q -X Q Y Q Z Q and camera coordinate system O C -X C Y C Z C If the coordinates of the point corresponding to point P are given, then C WorldCoordinate With C MonitorCoordinate The coordinate mapping relationship between them is as follows: In step 5, C WorldCoordinate With C MirrorCoordinate The coordinate mapping relationship between them is as follows: In step 6, C CameraCoordinate With C CheckerCoordinate The coordinate mapping relationship between them is as follows: In step 7, C WorldCoordinate With C CheckerCoordinate The coordinate mapping relationship between them is as follows: In step 8, C WorldCoordinate With C CameraCoordinate The coordinate mapping relationship between them is as follows: Where C WorldCoordinate =(x W ,y W ,z W ,1) T ; C MonitorCoordinate =(x L ,y L ,z L ,1) T ; C MirrorCoordinate =(x M ,y M ,z M ,1) T ; C CheckerCoordinate =(x Q ,y Q ,z Q ,1) T ; C CameraCoordinate =(x C ,y C ,z C ,1) T ; R1, R2, R3, R4 and R5 are all rotation matrices, and all are third-order square matrices; T1, T2, T3, T4, and T5 are all translation vectors, and are all three-dimensional column vectors; All are block matrices of the same type and coordinate transformation matrices, i = 1, 2, 3, 4, 5.

7. The pose calibration method for each component in the fringe reflectance measurement system according to claim 6, characterized in that: The T1 = (x t1 ,y t1 ,z t1 ) T T2 = (x t2 ,y t2 ,z t2 ) T T3 = (x t3 ,y t3 ,z t3 ) T T4 = (x t4 ,y t4 ,z t4 ) T T5 = (x t5 ,y t5 ,z t5 ) T x ti y ti z ti The values ​​are the x, y, and z directions of the new coordinate system relative to the old coordinate system, i = 1, 2, 3, 4, 5.

8. The pose calibration method for each component in the fringe reflectance measurement system according to claim 7, characterized in that: said R i =R x (i i )R y (f i )R z (ψ i ); in θ i Let φ be the x-axis rotation angle of the new coordinate system relative to the old coordinate system. i Let ψ be the y-axis rotation angle of the new coordinate system relative to the old coordinate system. i R is the rotation angle of the new coordinate system relative to the old coordinate system along the z-axis. x (θ i R is the rotation matrix in the x-direction of the new coordinate system relative to the old coordinate system. y (φ i R is the rotation matrix in the y-direction of the new coordinate system relative to the old coordinate system. z (ψ i ) is the rotation matrix in the z-direction of the new coordinate system relative to the old coordinate system, i = 1, 2, 3, 4, 5.

9. The pose calibration method for each component in the fringe reflectance measurement system according to claim 8, characterized in that: In step 3, establish the display coordinate system O. L -X L Y L Z L The specific steps are as follows: 1) Divide the screen of the display (3) into four equal parts in both the horizontal and vertical directions using six grid lines, with each grid line having a width of 1 pixel; 2) Using the laser tracker (11) and laser target ball (402), calculate and fit the plane containing the nine intersection points of the six grid lines, and determine the center point of the screen and the normal vector of the plane; 3) Use the center point of the screen as the monitor coordinate system O L -X L Y L Z L The origin of the plane is used as the normal vector of the display coordinate system O. L -X L Y L Z L Then, arbitrarily select the x and y axes to establish the display coordinate system O. L -X L Y L Z L .

10. The pose calibration method for each component in the fringe reflectance measurement system according to claim 9, characterized in that: In step 1, the display (3) is an LCD display with a screen resolution of 1280×800, and the camera is a CCD camera; the size of the checkerboard target plate (4) is 15mm×15mm, and the diameter of the laser target ball (402) is 0.5 inches.

Images